Yes, and this is how your site should be structured. Remove all your css and put into a file and save as style.css (you can name the stylesheet what you like and save it to the root of your site, as I am displaying here, or in a folder). Then, in your HTML page you link to the stylesheet in the head:
<head><!-- Other head code here --><link href="style.css" rel="stylesheet" type="text/css" /></head>
If I understand correctly, you're not looking for external CSS files (which should be external, as the poster above pointed out), but you have multiple pages that have the exact same code in them. The best way to do this is through PHP templates. You can have one PHP file with all the common HTML code in it, and just call that PHP file when you need the common code. You can then edit your PHP file, and the changes will reflect globally on all pages.